The superconductor-insulator transition in the presence of strong compensation of dopants was recently realized in La doped yttrium barium copper oxide. The compensation of acceptors by donors makes it possible to change independently the concentration of holes $n$ and the total concentration of charged impurities $N$. We propose a theory of the superconductor-insulator phase diagram in the $\left(N,n\right)$ plane. It exhibits interesting features in the case of strong coupling superconductivity, where Cooper pairs are compact nonoverlapping bosons. For compact Cooper pairs the transition occurs at a significantly higher density than in the case of spatially overlapping pairs. We establish the superconductor-insulator phase diagram by studying how the potential of randomly positioned charged impurities is screened by holes or by strongly bound Cooper pairs, both in isotropic and layered superconductors. In the resulting self-consistent potential the carriers are either delocalized or localized, which corresponds to the superconducting or insulating phase, respectively.

• Received 22 December 2008

DOI:https://doi.org/10.1103/PhysRevB.79.134504